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Simplifying 25x2 + -56x = 16 Reorder the terms: -56x + 25x2 = 16 Solving -56x + 25x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + -56x + 25x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -56x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.64 + -2.24x + x2 = 0 Move the constant term to the right: Add '0.64' to each side of the equation. -0.64 + -2.24x + 0.64 + x2 = 0 + 0.64 Reorder the terms: -0.64 + 0.64 + -2.24x + x2 = 0 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.00 + -2.24x + x2 = 0 + 0.64 -2.24x + x2 = 0 + 0.64 Combine like terms: 0 + 0.64 = 0.64 -2.24x + x2 = 0.64 The x term is -2.24x. Take half its coefficient (-1.12). Square it (1.2544) and add it to both sides. Add '1.2544' to each side of the equation. -2.24x + 1.2544 + x2 = 0.64 + 1.2544 Reorder the terms: 1.2544 + -2.24x + x2 = 0.64 + 1.2544 Combine like terms: 0.64 + 1.2544 = 1.8944 1.2544 + -2.24x + x2 = 1.8944 Factor a perfect square on the left side: (x + -1.12)(x + -1.12) = 1.8944 Calculate the square root of the right side: 1.376372043 Break this problem into two subproblems by setting (x + -1.12) equal to 1.376372043 and -1.376372043.Subproblem 1
x + -1.12 = 1.376372043 Simplifying x + -1.12 = 1.376372043 Reorder the terms: -1.12 + x = 1.376372043 Solving -1.12 + x = 1.376372043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.12' to each side of the equation. -1.12 + 1.12 + x = 1.376372043 + 1.12 Combine like terms: -1.12 + 1.12 = 0.00 0.00 + x = 1.376372043 + 1.12 x = 1.376372043 + 1.12 Combine like terms: 1.376372043 + 1.12 = 2.496372043 x = 2.496372043 Simplifying x = 2.496372043Subproblem 2
x + -1.12 = -1.376372043 Simplifying x + -1.12 = -1.376372043 Reorder the terms: -1.12 + x = -1.376372043 Solving -1.12 + x = -1.376372043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.12' to each side of the equation. -1.12 + 1.12 + x = -1.376372043 + 1.12 Combine like terms: -1.12 + 1.12 = 0.00 0.00 + x = -1.376372043 + 1.12 x = -1.376372043 + 1.12 Combine like terms: -1.376372043 + 1.12 = -0.256372043 x = -0.256372043 Simplifying x = -0.256372043Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.496372043, -0.256372043}
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